Parametric analysis of transient stability in power systems using classical models

This thesis aims to strengthen the bridge between mathematical and practical research into the transient stability of power systems. Literature that exploits the mathematical parallels between models for transient dynamics in power systems and the phenomenon of synchronisation in complex networks is explored. However, it is contended that research at the intersection of complex systems and power system stability can limit its applications to practical issues in power engineering. This thesis focuses on the measurement of transient stability in power systems in terms of a traditional stability metric for short-circuit faults on a power network, the critical clearing time (CCT). The CCT provides an upper bound on the duration of a short circuit on a power network before it is removed - cleared - by the action of protection mechanisms to isolate the faulted circuit such that the system will regain synchrony once the fault is cleared. Approaches that use energetic methods for assessing the transient stability of a power system are extended by developing metrics that can measure stability trends for different scenarios in a power system via the numerical continuation of equilibrium configurations under the variation of system parameters. An analytical CCT (ACCT) approximation is derived from this energetic framework in order to capture trends in stability with respect to a system parameter. The performance of the ACCT is compared to more accurate computations of CCT that use slower numerical simulation techniques. Attention is given to how well the ACCT approximation can capture stability trends under variation of key network design parameters such as load admittance and generator inertia. It is found for a two-machine infinite bus (TMIB) system that load parameter values that can improve stability can be identified using the ACCT. Also, the general dependence of a fault's CCT on the inertia of a generator in a TMIB power system is identifiable using the ACCT. For power systems with stationary generator inertia values, a method to provide a contingency analysis of fault locations is proposed. The method ranks the locations of short-circuit faults by their CCT; the more severe a fault the shorter its CCT. It is found in a TMIB system that the ACCT can identify the general location of severe faults under different inertia scenarios. It is shown that in larger power systems, energetic methods can be used to accurately identify the locations of faults with short CCTs. These results, together with relevant literature are used to suggest possible strategies to monitor transient stability within modern power systems.